1. Field of the Invention
The present invention relates to resistors for semiconductor devices, and more particularly to diffused resistors for integrated circuits.
2. Description of the Prior Art
In general, a resistor is used as a passive element in a integrated circuit (IC). A diffused resistor is one well known type of such resistor. The structure of a typical diffused resistor is shown in FIGS. 1a and 1b. FIG. 1a is a schematic cross-sectional view of the resistor and FIG. 1b is a schematic plan view taken on line I--I, in FIG. 1a. On a p-type semiconductor substrate 1 (FIG. 1a), an n.sup.+ -type buried layer 2 and an n.sup.- -type epitaxial layer 3 are formed. A portion of the epitaxial layer 3 is isolated from the rest of the epitaxial layer 3 by surrounding it with a p.sup.+ -type isolating region 5, as shown in FIG. 1b, to form an n.sup.- -type isolated region 4. In the isolated region 4, a p.sup.+ -type diffused region (i.e. a resistance layer) 6 and an n.sup.+ -type diffused region (i.e. a contact layer) 7 are formed. An insulating layer 8 covers the epitaxial layer 3 except for the contacting surfaces for terminals 9, 10 and 11, as shown in FIGS. 1a and 1b. A desired resistance of the resistance layer 6, i.e. of the diffused resistor layer, can be obtained by determining the length (L) and the width (W) (FIG. 1b) of the resistance layer 6 between the terminals 9 and 10. When the electric current flows in the resistance layer 6, the p-n junction between the resistance layer (i.e. the p.sup.+ -type diffused region) 6 and the n.sup.- -type isolated region 4 is always reverse biased by connecting the terminal 11 to a potential that is more positive than potentials of the terminals 9 and 10 of the resistance layer 6. A diffused resistor such as the above-mentioned is described in, for example, Paul R. Gray, Robert G. Meyer: Analysis and Design of Analog Integrated Circuits, (1977), pp. 99-103 [John Wiley & Sons, Inc.].
When the p-n junction is reverse biased, a depletion layer is generated in the both sides of the p-n junction interface. In the case of the above-mentioned diffused resistor, since there is a potential difference between the terminals 9 and 10 of the resistance layer 6, the thickness of the depletion layer below the terminal 9 is different from that of the depletion layer below the terminal 10. If the potential of the terminal 9 is lower than that of the terminal 10, the thickness of the former depletion layer is greater than that of the latter depletion layer. The thickness of the depletion layer decreases along the length (L) of the resistance layer 6 in the direction from the terminal 9 to the terminal 10. Accordingly, a resistance value (r) per unit length of the resistance layer 6 varies, as indicated by a solid line A of FIG. 2. In FIG. 2 symbols "a" and "b" indicate the spot of the terminal 9 and the spot of the terminal 10, respectively. In this case, the resistance (R.sub.A) of the diffused resistor is obtained by calculating the shaded area of FIG. 2.
If the potential of the terminal 9 is decreased, namely, when a voltage applied across the terminals 9 and 10 is increased, the thickness of the depletion layer below the terminal 9 become thicker. Accordingly, the resistance value (r) per unit length at the terminal 9 becomes larger compared to the above-mentioned case. The resistance value (r) per unit length varies, as indicated by a broken line B of FIG. 2. In this case, the resistance (R.sub.B) of the diffused resistor becomes larger than the resistance (R.sub.A) of the above-mentioned case. If the potential of the terminal 9 is increased in the same level of the potential of the terminal 10, the resistance value (r) per unit length of the resistance layer 6 becomes constant, as indicated by a broken line C of the FIG. 2. In this case, the resistance (R.sub.C) of the diffused resistor becomes smaller than the resistance (R.sub.A) of the above-mentioned case.
As is clear from the above-described explanation, the resistance (R) of the diffused resistor varies according to the voltage applied across the terminals 9 and 10 of the resistance layer 6. It is easily possible to maintain a positive voltage applied to the isolated region 4 of the epitaxial layer 3 at a constant value. For example, it is preferable to connect the terminal 11 to a positive terminal of a power source, so that the isolated region 4 has the most positive potential in the integrated circuit. However, the voltage applied across the terminals 9 and 10 is changed during the operation of the integrated circuit. The relationship between the current flowing in the resistance layer 6 and the voltage applied to the resistance layer 6 is indicated by a solid curve D in FIG. 3, for the case where the voltage is increased by reducing the potentional of the terminal 9. Such a relationship is caused by increasing the resistance of the resistor along with an increase in the voltage.